TD 225 
. B8 P2 
1858a 
Copy 1 





BROOKLYN WATER WORKS. 


REPORT 


ON THE POSITION OF THE 



WITH NOTES OF CERTAIN EXPERIMENTS MADE ON THE WATER 
DELIVERIES OF PORTIONS OF THE CROTON AND THE 
JERSEY CITY PIPE MAINS. 


18 5 8 . 


NEW YORK: 

HOSFORD & CO., PRINTERS AND STATIONERS, 

5 7 & 59 William Street. 


































































BROOKLYN WATER WORKS. 


REPORT 


ON THE POSITION OF THE 


osptd Jill (Kit gnu Joust, 


WITH NOTES OF CERTAIN EXPERIMENTS MADE ON THE WATER 
DELIVERIES OF PORTIONS OF THE CROTON AND THE 
JERSEY CITY PIPE MAINS. 








18 5 8 . 



NEW YORK: 

HOSFORD & CO., PRINTERS AND STATIONERS, 

57 & 59 William Street. 


1 8 5 8 . 













Engineer’s Office, Brooklyn Water Works, 
November 8th, 1858. 

JOHN H. PRENTICE, Esq., 

President: 

Sir —As it will soon become necessary to select a site for the 
Prospect Hill Engine House, I beg to make a statement of the 
reasoning which has assisted me in determining the height 
above tide water, at which I would propose to place it. 

The Pump Well of the Prospect Hill Engine House is to be 
supplied with water by a branch pipe from the 36 inch main 
which has just been laid in De Kalb Avenue; a part of this 
branch pipe will be of 30 inches diameter, and part of 20 
inches. 

It is a difficult point to determine exactly the height on the 
Prospect Hill slope, at which the required amount of water 
(156,250 gallons per hour) for that secondary service can be 
delivered, under all the conditions of the city consumption. 

During the first or second season after the receipt of water 
into the city, when its use by the citizens will be comparatively 
limited, a difference of level of but 20 feet below the water of 
the Ridgewood Reservoir would probably secure the desired 
delivery on Prospect Hill; but this difference would become en¬ 
tirely insufficient, when the use of the water in the city became 
as general as it now is in the City of New York. 

I have assumed that the Prospect Hill Pump Well should be 
situated low enough to secure a sufficient delivery of water 


4 


there when the flow through the 36 inch main, laid from Ridge¬ 
wood Reservoir, is equal to the flow at this time through the 
same size of main into New York. 

From experiments made recently by Mr. G. S. Greene, with 
Mr. Craven’s permission, on the New York Works, to ascer¬ 
tain, among other points, the delivery of the two 36 inch mains 
from the Receiving Reservoir at Eighty-sixth Street into the 
Distributing Reservoir at Forty-second Street (see Note 1), the 
flow into the city by each of the two effluent mains (36") which 
convey the water from the south side of the Distributing Res¬ 
ervoir for the city consumption, was ascertained to be 647,101.5 
cubic feet during the eight hours between 10 A. M. and 6 P. M. 
of Saturday, the 10th of July, 1858, = 22.469 cubic feet per 
second. 

For the twelve hours of day between 6 A. M. and 6 P. M., 


assuming the same rate of delivery to prevail, 

This would give. 970,652 cub. ft. 

For the twelve night hours, assume the con¬ 
sumption to be one fourth of the above, viz... 242,663 “ 


Total flow in 24 hours for this 36 inch pipe .. 1,213,315 “ 

The Croton water is delivered from the Re¬ 
ceiving Reservoir aforesaid into New York by 
four mains, two of 36 inches diameter each, 
and two of 30 inches diameter. 

The aggregate consumption of the City of 
New York at the above rate would sum up as 
follows: 

The second 36 inch main.1,213,315 “ 

Flow through the two 30 inch mains, nearly in 
proportion to the areas of the 36 inch and 
30 inch pipes, or more accurately, as Vd 5 1,538,333 “ 

Total daily consumption in cubic feet.3,964,963 









5 


This is equal to 24,781,019 imperial gallons, or 80,976,273 
New York gallons, in twenty-four hours. 

It has been shown that the delivery of the 36 inch main into 
New York during the twelve hours of the day, amounts to 
970,652 cubic feet, = 7,583,219 New York gallons. 

I will assume the 36 inch main from the Ridgewood Res¬ 
ervoir to be delivering at this rate into Brooklyn and Wil¬ 
liamsburg, when the Pump Well at Prospect Hill is receiving 
its quota of water. 

This would make the delivery per hour from Ridgewood 
Reservoir 631,935 gallons, say 632,000 New York gallons. 

Assuming one fourth of this quantity to pass on by the 30 inch 
branch main to Williamsburg, there would flow on into Brook¬ 
lyn proper a rate per hour of 474,000 gallons. 

The Prospect Hill pumping engine is required to be of suf¬ 
ficient capacity to raise 156,250 gallons per hour, and must con¬ 
sequently be supplied at that rate—call the rate 166,666 gallons 
per hour through its supply pipe, to allow for the effect of the 
two 12 inch branches upon this pipe, one at Gates Avenue and 
the other at Fulton Avenue. 

Applying the proper distances, we have now the following data: 

15,637 feet of 36 inch main, between Ridgewood Reservoir 
and the junction of De Kalb Avenue with Division Avenue, de¬ 
livering at the rate of 632,000 gallons per hour. 

10,425 feet of 36 inch main, from the last mentioned point 
along De Kalb Avenue to the crossing of Washington Avenue, 
delivering at the rate of 474,000 gallons per hour. 

4,600 feet of 30 inch and 20 inch main, from the last point to 
the supposed position of the pump well, delivering at the rate 
of 166,666 gallons per hour. 

Assuming, in the first place, the above mains or pipes to be 
straight and unbroken by branches, the following table will 
show the calculated head necessary to produce the rates of flow 
above indicated. 


Table 


6 



-+-) 

03 

.03 

4+-t 



CO 

£— 

Jr- 

Ir- 

o 

CD 

CO 

Oi 

OS 

CD 

CO 



r—i 

r—1 

lO 

rH 

CO 


r—H 

CO 

oi 

r—< 

r—1 

rH 

Os 


◄ 


Rate of Flow, 
in cubic feet 
per second. 

22.471 

16.853 

5.9259 

5.9259 

Rate of Flow, 
in N. Y. gallons 
per hour. 

632,000 

474,000 

166,666 

166,666 

Diameter 
of 'Pipe, 
in inches. 

36 

36 

30 

20 

Length of 
Pipe, 
in feet. 

15,637 

10,425 

3,000 

1,600 

30,662 


SzJ 

O 

i—i 

H 

o 

o 

- 



• ri 


O. 


• U1 

• c3 


-4—> 

w 



03 

03 

03 

• O 
. 

03 

0 

03 

P 

• 03 


to 

• 0 
• 0 

. 03 

0 

0 

03 

rH 


<D 

-^.§e£ 


O 

!> 


co rri 
03 ^ 

tf 


K* 

03 
^ n 

9 cj ' 

W 

03 


be o 
cJ P-i 
• H fl 
bc~ 3 


CO - 
00 — 

r^i fe: 

P r*- 


The above formula is derived from a formula of Prony’s, which has been altered in its constants, so as to 
correspond very nearly with the results of recent experiments on the ordinary deliveries of the connect¬ 
ing pipes of the New York Reservoirs and of the Jersey City Reservoirs. 


















1 


The head required to produce, under the given circumstances, 
the necessary delivery at the Prospect Hill pump well, accord¬ 
ing to the New York and Jersey City experiments, is. 49.52 feet. 
For the effect of the branch pipes to be connected 


hereafter with these mains, add.10.00 “ 

Total head lost. 59.52 “ 


This last mentioned allowance of 10 feet will be adverted to 
again. 

The surface of Ridgewood Reservoir, when full, is 170 feet 
above mean high water of Brooklyn Harbor. Assume that the 
height of water in the Reservoir (except in extreme cases) is 

not allowed to fall below.164.0 feet. 

Deduct the head lost as above.;. 59.5 “ 

Height of water in Prospect Hill Pump Well above 

tide..104.5 “ 

The floor of the Engine House may be situated 12 or 

15 feet above the water of the Pump Well, say.. 15.0 “ 

Height of this floor above tide.119.5 “ 

The ground for the site of the Engine House may be conven¬ 
iently 4 or 5 feet below the level of this floor, say 115 feet. 

This height of 119.5 feet, if our calculations are correct, 
should enable you to control a liberal supply of water at the 
Prospect Hill Engine House, when the delivery of the 86 inch 
main into Brooklyn is about its maximum in practice. 

Another line of similar pipe from the Reservoir will, in all 
probability, be laid before the rate of flow into the city, which 
has-been assumed for this one, is exceeded. 

In the interim, the free delivery at the Prospect Hill Pump 
Well would begin, as already stated, by being much in excess of 










8 


the contract requirements, but would approximate with every 
additional year more nearly to our calculations. The excess of 
head during the early years can be controlled by the stop-cock, 
and might be used to assist the action of the engine and reduce 
the consumption of fuel. 

To enable me to understand how much to allow beyond the 
results which any calculations can well give for the confusing 
influences of the various connecting pipes hereafter to be ap¬ 
plied on this section of the city “ distribution/’ I made, with Mr. 
Craven’s permission, two experiments on the New York City 
mains, at points near the centre of the city. 

One of the 36 inch delivering mains of the Distributing Res¬ 
ervoir passes down the Fifth Avenue into Broadway, and down 
Broadway to opposite Houston Street, where it is reduced to 
a 30 inch main, which last continues down Broadway to about 
opposite the Hospital. 

At Canal Street a 20 inch pipe branches from the 30 inch 
main last mentioned. Upon this 20 inch pipe, within 12 feet 
of the 30 inch main, I placed an Ashcroft guage, and had its in¬ 
dications noted every quarter hour between 7 A. M., and 5 
P. M., of the 23d of July last. 

The readings varied from 26 lbs. at 7 A. M., to 24± lbs. at 
9 and 10 o’clock, A. M.; thence back to 26J lbs. at 5 P. M. 
The average and more general reading was 25 lbs., equal to a 
head of 57 feet. 

The distance of this point from the Distributing Reservoir is 
13,130 feet, and from the Receiving Reservoir 24,430 feet, all 
of which length consists of 36 inch pipe, with the exception of 
about 2,300 feet of 30 inch pipe between Houston and Canal 
Streets. Between the Distributing Reservoir and Canal Street, 
(13,130 feet) branch pipes connect at intervals, as hereinafter 
enumerated. 


9 


The height of the Receiving Reservoir above tide, when full, 

as it was in this instance, is.114.0 feet. 

The height of the pipe in question at this point (Canal 

Street) above tide... 4.5 “ 

The difference in level, therefore.109.5 “ 

Guage indication of head available at Canal Street.. 57.0 “ 

Loss of head. 52.5 “ 


In this case 52^ feet of head are absorbed in a distance of 
4.63 miles. 

The distance between the Ridgewood Reservoir of the 
Brooklyn Water Works and the Prospect Hill Engine House 
is 5.81 miles. 

The other experiment was made on the 30 inch main in 
Avenue A, opposite Tompkins Square. 

This 30 inch main, after leaving the vaults of the Receiving 
Reservoir, follows down Fifth Avenue to Seventy-ninth Street, 
thence along Seventy-ninth Street to Third Avenue, along Third 
Avenue to Fourteenth Street, along Fourteenth Street to Ave¬ 
nue A, and along Avenue A to Tompkins Square. 

The distance along its line from the Receiving Reservoir to 
the point where the Ashcroft guage was applied, is 23,400 feet. 
The distributing pipes branching from it are shown in the ac¬ 
companying sketch. 

The guage indicated an average pressure of 25J lbs., equal 
to a head of 58 feet. 

The difference in level between the surface of the water in 
the Receiving Reservoir and the 

Pipe at this point is...102 feet. 

Average head, by the guage, available at Tompkins 

Square. 58 “ 

44 “ 


Loss of head 











10 


In this case 44 feet of head are absorbed in a distance of 
4.43 miles. 

In Table D, I have divided that part of the Fifth Avenue and 
Broadway main, applicable to our experiment, into two sections, 
viz.: the portion between the two Reservoirs, and the portion 
between the Distributing Reservoir and Canal Street. 

The first length measures 11,217 feet, and the difference of 
level of the surface waters of the two Reservoirs averaged, 
during Mr. Greene’s experiment, 20.215 feet. 

The second length measures 13,130 feet, and the difference of 
level between the surface of the water in the Receiving Reser¬ 
voir and the surface of the pipe in Canal Street, is 109.5 feet. 

In this Table, I have compared the actual head in practical 
use, as ascertained in the first section by levelling and in the 
second by the guage, with the calculated heads which some of 
the best formulas show, under the supposition of an unbroken 
pipe line and certain given deliveries. 

On the first section of the 36 inch main between the two 
Reservoirs, there were no side connections open to interfere 
with the regular flow in the pipe during the time of the experi¬ 
ment already mentioned (see Note 1). 

It will be observed that in this first section the calculated 
head (20.17) by the assumed formula “I” in column 8, necessary 
to pass the water which was delivered by each 36 inch main, 
agrees very nearly with the actual head 20.2, as obtained by 
levelling between the two surfaces. The well established 
formulas of columns 9 and 10, give 14.90 and 14.83 for the re¬ 
quisite head. 

The formula (“I”) referred to, is derived from one of Prony’s, 
the constants of which have been modified, so as to render it an 
exponent of the experiments made on the New York and the 
New Jersey mains, as will be further explained. 

In the portion of the main below the Distributing Reservoir, 


Tabular Statement in regard to the Experiments upon the Hew York Mains. D. 


1 

3 

3 

4 

d 

0 

7 

8 

9 

10 

Head lost, 
in feet. 

How ascertained. 

Difference in level 
between the points, 
in feet. 

Delivery in N. Y. 
Gallons per hour. 

Delivery in cubic 
feet per second. 

Length of Pipe, 
in feet. 

Diameter of Pipe, 
in feet. 

Calculated head to produce the given 
flow, bv the formula, 
h=0.0004G‘I49L (v+0.397) s 

(L) 

Calculated head to produce 
the given flow, by Prony’s 
formula (2). 

(JD.) 

Calculated head to produce 
the given flow, by Hawkes- 
ley’s formula. 

' (A.) 


SECTION 1. Pipe Main between the Receiving Reservoir and the Distributing Reservoir. 


By levelling 
between the Res¬ 

20.215 

596,352 

21.2036 

11,217 

3 

20.1670 

20.1670 

14.899 

14,833 

ervoir surfaces. 











SECTION 2. Pipe Main between the Distributing Reservoir (down Broadway) and Canal Street. 

The total distance is divided up, as in column 6, (or convenience of calculation. 




89.28 


632,000 

570,000 

480,000 

420,000 

350,000 

22.471 

20.267 

17.067 

14.933 

12.444 

3,050 

2,250 

2,850 

2,650 

2,330 

3 

3 

3 

3 

2.5 

6.0778 

3.7357 

3.5103 

2.6008 

3.7461 


4.5175 

2.7371 

2.5032 

1.8113 

2.6925 

4.6938 

2.8670 

2.5389 

1.8148 

2.7792 

52.5 

By an Ashcroft 

109.5 






19.6707 

19.6707 




guage applied to 












the pipe. 








39.8377 




Similar Statement for the Mean of Experiments upon the 20 inch Main of the Jersey City Water Works. 


| How ascertained. 

Actual head, 
in feet. 

Delivery in N. Y. 
Gallons per hour. 

Delivery in cubic 
feet, per second. 

Length of Pipe, 
in feet. 

Diameter of Pipe, 
in feet. 

Calculated head to produce the given 
flow, by the formula, 
h=0.00046749i (v+0.397) 8 

A 

Calculated head to produce 
the given flow, by Prony’s 
formula (2). 

(D.) 

Calculated head to produce 
the given flow, by Hawkes- 
ley’s formula. 

(A.) 

By levelling 

28.1285 i between the Res- 
| ervoir surfaces, 
il 

28.1285 

88,231.5 

3.13712 

29,715 

1.6667 

28.064 

17.921 

16.056 




































































































































ns. The Jersey City Main is enlarged, for a distance of 128 feet, 


}f the delivery by experiment of the Jersey City Main, to make a 


3 follows: (See Sketch S.) 


fc. The reduced flow, beyond the several points where the pipes 


nts 


h=0.00046749—(v+0.397)* 


11 


where the distributing pipes for the city consumption radiate 
from it on either side, the actual head absorbed between this 
Reservoir and Canal Street, in producing the flow occurring 
there, is 32.28 feet. Assuming the pipe to be straight, and the 
quantities to be as in the table, the calculated head required to 
produce the same flow of water, is by formula “I” 19.67 feet— 
showing a difference of 12.61 feet. 

The difference by the other formulas is much greater. 

The great difference in this case between calculation and 
the guage indication, must be attributed largely to the effect of 
the many connecting pipes which occur on this section, involv¬ 
ing eddies inside the pipe, and confused action, which these 
formulas were not intended to express; but there must be other 
reasons growing out of circumstances connected with the condi¬ 
tion of the pipe, unknown to me, producing this large difference: 
these circumstances, however, might obtain on the Brooklyn pipe 
also, and it has been thought best, therefore, to make an allow¬ 
ance for them. 

The accompanying sketch S will show the position of the 
branching pipes known to me, as well as their sizes. 

There are five 20 inch pipes branching from the west side of 
this 36 inch main, and three from the east side, being eight 20 
inch pipes in all, drawing their supplies from this main between 
the defined points. 

These eight pipes have a water area of 17.45 square feet. 

The delivery area of the main, when it leaves the Distribut¬ 
ing Reservoir, is 7.07 square feet: when it reaches Canal Street 
it has virtually increased to the united areas of one 30 inch 
pipe and eight 20 inch pipes, equal to 22.36 square feet of 
water space. 

The loss of head resulting from this rapid enlargement, in 
effect, of the original main, could be counteracted and to a cer¬ 
tain extent neutralized by a liberal addition of auxiliary mains 


12 


from the Reservoirs, and of cross mains throughout the small 
pipe distribution. 

This kind of correction of the difficulty has already been begun, 
but it will involve, probably, an increased expenditure of water. 

So far as the loss of head may result from accidental collec¬ 
tions of air in the pipes, it could to that extent be remedied by 
a more liberal supply and more frequent use of air-cocks. 

The reasons will now be understood which influenced me in 
making an allowance of 10 feet for the effect of branches, &c., 
in the calculations of head required to secure the Prospect Hill 
supply. 

The branchings in this case are not likely, for a very long 
time, to equal in extent those on the New York section referred 
to, and I have not, therefore, allowed as much. 

To recapitulate, 

1st. In a distance of 4.63 miles on the New York 36 inch 
main the head lost is 52J feet. 

2 d. In a distance of 4.43 miles on the New York 30 inch 
main the head lost is 44 feet. 

(The guage varied considerably in this experiment on the 30 
inch main. The morning readings would have given a much 
greater loss than the above.) 

3d. In a distance of 5.81 miles of 36, 30, and 20 inch pipes in 
the Brooklyn case referred to, the loss of head will amount, it 
is calculated, to 56 feet, some five to ten years hence, when the 
use of the water has become very general throughout the city. 

The experiment made upon the two Croton Reservoirs, to as¬ 
certain the actual delivery of the two intervening 36 inch 
mains under a given head, gave results considerably below 
those which the usual formulas would have promised under the 
same conditions. 

The discrepancy may have grown out of various causes of 


13 


disturbance to which all lines of pipes are subject, some of these 
beyond the reach of correction, and others controllable by the 
exercise of constant care and attention. 

Among the first may be instanced the tubercular corrosion, 
which on these pipes is considerable, as I have ascertained by 
inspection. 

Among the second may . be instanced the collection of air on 
the high points of the line, and some sedimentary deposits at 
low points. 

Both of these last causes might have been more or less got rid 
of by blowing off at the depressions when there exists the means 
of doing so, and by opening the air-cocks which are provided, 
and adding others where necessary. 

But the experiment was more interesting and pertinent to the 
case in point without such previous preparation of the pipes. 
It was desirable to understand the rate of flow under the ordi¬ 
nary condition and superintendence of the service, rather than 
under a special condition of it. 

To ascertain whether the discrepancy adverted to was excep¬ 
tional, or whether it arose more or less from some speciality in 
the character of this experiment, I have had, with the consent 
and assistance of Mr. G. H. Bailey, the Engineer of the 
Jersey City Water Works, a somewhat similar experiment 
made on the pipe which connects the two Reservoirs of these 
Water Works, the one situated near Belleville, the other in 
Hudson City. 

The length of the pipe connecting these two Reservoirs is 
29,715 feet. 

The diameter is 20 inches, except at the crossing of the 
Hackensack River, where it is increased to 24 inches for 128 
feet of its length. 

During the experiment no water was received into the Belle¬ 
ville Reservoir from the Pumping Engine. 


14 


At the beginning of the experiment the difference in level of 
the surface water of the two Reservoirs was 80.529 feet. 

At the end of the experiment it was 25.646 feet. 

The experiment was made on the 25th, 26th, and 27th of Sep¬ 
tember, 1858. 

Mr. C. W. Boynton, one of our assistant engineers, took the 
principal observations, and has made for me the calculations 
presented in Table J. 

In this Table we have brought together a number of well- 
known formulas, and compared the velocities which they give 
for the head and size of pipe, with the actual velocity as ob¬ 
tained from this experiment (see Note 2): the same comparison 
is there made with the results of the Croton Reservoir experi¬ 
ment. 

It will be seen that in both cases all these formulas gave ve¬ 
locities considerably greater than the actual velocity which pre¬ 
vailed in each experiment. 

The Jersey Reservoir experiment, therefore, corroborates the 
Croton Reservoir experiment, in giving deliveries and velocities 
below the quantities which the formulas gave. 

Preferring to take these experiments for my guide, the cir¬ 
cumstances of which elucidate so well the case which is pre¬ 
sented on the Brooklyn Works, I have had one of Prony’s 
formulas modified in its constants, to meet very nearly the re¬ 
sults of both experiments, and have used it as thus modified to 
ascertain the probable loss of head in the Brooklyn case al¬ 
ready detailed. 

This exceptional equation (given elsewhere) has also been 
transformed for our convenience so as to express the head re¬ 
quired under the conditions defined, instead of the velocity. 

The modified form of Prony’s formula I do not introduce as 
applicable elsewhere, or as a correction of well-established 


Tabular Comparison of the New York and Jersey City Experiments. J. 








VALUES OF THE VELOCITY, IN FEET PER SECOND. 



-EjjVJt JlixvlMiliJN 1& : 

Where, and by whom, made. 

Diameter of the 
Pipe, in feet. 

Length of Pipe, 
in feet. 

under which the 
discharge occurred. 

As deduced from 
the discharge. 

By Hawkesley’s 
formula. 

(A.) 

By Blackwell’s 
formula. 

m 

By Prony’s 
formula (1). 
(C.) 

By Prony’s 
formula (2). 
(D.) 

By Eytelweiu’s 
formula. 

(E.) 

By D’Aubuisson’s 
formula (1). 

m 

By D’Aubuisson’s 
formula (2). 
(G.) 

By Weisbach’s 
formula. 

(H.) 

On the 20 inch Main between the Reservoirs 

l 1.6667 

29,715 

30.262 

1.4924 

1.97399 

1.97624 

1.9206 

1.91068 

1.97063 

1.927302 

1.92923 

2.03255 

of the Jersey City Water Works. 

\ 1.6667 

29,715 

29.758 

1.51337 

1.9575 

1.9597 

1.9039 

1.89338 

1.95416 

1.9105 

1.9123 

2.01294 

By G. H. Bailey and C. W. Boynton. 

J 1.6667 

29,715 

29.317 

1.44893 

1.94293 

1.94514 

1.8891 

1.87838 

1.93963 

1.8957 

1.8976 

1.99688 

128 feet of this Main is 24 inches diameter. 

) 1.6667 

'29,715 

28.365 

1.45795 

1.91112 

1.9133 

1.8570 

1.8453 

1.90789 

1.8632 

1.8650 

1.95938 

Allowance is made in the calculation for this 

/ 1.6667 

29,715 

27.302 

1.39107 

1.8750 

1.877115 

1.8204 

1.8077 

1.87180 

1.8263 

1.8282 

1.91797 

enlargement, and the curves in the pipe. 

1.6667 

29,715 

26.325 

1.381155 

1.84115 

1.84323 

1.7861 

1.7726 

1.83801 

1.7918 

1.7936 

1.87943 

Jersey City Water Works. Mean result. 

1.6667 

29,715 

28.1285 

1.43795 

1.90031 

1.9053 

1.8489 

1.837 

1.8999 

1.855 

1.857 

1.9502 

New York 36 inch Main between Receiving 
and Distributing Reservoirs. By G. S. 
Greene. This pipe has three right angled 
curves of 90 feet radius, which are taken 
into account in the calculation. 

3.0 

11,217 

20.215 

2.99967 

3.5016 

3.5230 

3.484 

3.514 

3.4917 

3.4891 

3.506 

3.848 


The formula, which very closely expresses the results of the New York and the Mean of the Jersey City Experiments, is: v=46.2502^-^ —0.397, whence, h=0.00046749y- (v+0.397) 8 
































































Comparison of Calculations from Established Formulas, with the Results of Various Experiments on Pipes. M. 


EXPERIMENTS: WHERE, AND BY WHOM, MADE. 


Jersey City Water Works. Main from the Belleville Reservoir to the Hudson City 
Reservoir. By G. H. Bailey and C. W. Boynton. Of this Main 128 ft. is 24 
inches diameter. Correction for this enlargement, as also for the curves, is made 
in the calculation.. 


Jersey City Water Works. Mean result 


Croton Aqueduct. Main from the Receiving Reservoir to the Distributing Res¬ 
ervoir. By G. S. Greene. There are in this Main three right angled curves 
of 90 ft. radius, for which allowance is made in the calculations. 


Crawley Pipe. Crawley to Edinburgh. Experiment by Mr. James Leslie. 


Colington Pipe. From Clubbie Dean Reservoir to Castle Hill. By Mr. Leslie, 
Do. From Torduff Cistern to Castle Hill. do. do. 

Do From Clubbie Dean Reservoir to Torduff Cistern. do. 


Main from Belvidere Road to Brixton. By Mr. 


Do. 

Do. 

Do. 

Do. 

Do. 


do. do. 

do. do. 

do. do. 

do. do. 

from Ditton to Brixton. 


James S 
do. 
do. 
do. 
do. 
do. 


impson 


1 

Character 
of the 
Water. 

Age of the 
Pipe laid, 
in years. 

Diameter of Pipe, 
in feet. 

Length of Pipe, 
in feet. 

Head of Water, 
in feet. 

VELOCITIES, IN FEET PER SECOND. 

As taken from 
the Experiments. 

By Prony’s 
formula (2). 
(D.) 

By D’Aubuisson’s 
formula (1.) 

(F.) 

By Hawkesley’s 
formula. 

(A.) 

By Eytelwein’s 
formula. 

(E.) 

Soft. 


20 in.=1.6667 

29,715 

30.262 

1.4924 

1.91068 

1.927302 

1.97399 

1.97063 

Soft. 

4 

1.6667 

29,715 

29.758 

1.51337 

1.89338 

1.9105 

1.9575 

1.95416 

Soft. 

4 

1.6667 

29,715 

28.1285 

1.43795 

1.837 

1.855 

1.90031 

1.8999 

Soft. 

16 

86 in.=3.0 

11,217 

20.215 

2.99967 

3.514 

3.4891 

3.5016 

3.4917 

Soft. 

29 

15 in.=1.25 

44,400 

226. 

3.4634 

j 3.833 


3.8268 


Soft. 

8 

16 in.=V333 

29,580 

420. 

6.8158 

6.7199 


6.59805 


Soft. 

8 

1.333 

25,765 

230. 

5.2521 

5.291 


5.2307 


Soft. 


1.333 

3,815 

184. 

14.5030 

12.498 


12.062 


Hard. 


19 in.=1.58333 

22,440 

•41.0 

2.73411 

2.5367 


2.5775 


Hard. 


1.58333 

22,440 

43.5 

2.80183 

2.6173 


2.6549 


Hard. 


1.58333 

22,440 

34.0 

2.5225 

2.2971 


2.3472 


Hard. 


1.58333 

22,440 

27.5 

2.2601 

2.0514 


2.11095 


Hard. 


1.58333 

22,440 

24.0 

2.0569 

1.9070 


1.9720 


Hard. 


30 in.=2.5 

54,120 

25.0 

1.7690 

1.5502 


1.6296 



Note.— The Crawley Pipe is of three sizes, viz.: 20, 18, and 15 inches diameter, 
results from the formulas. 


It has been calculated above as if of 15 inches diameter throughout. 


A closer calculation would give a greater difference between the actual delivery and the 







































































































15 


formulas, but simply as an expression from the results of the 
particular experiments made this season, by which I prefer to 
be ruled in our own case. 

Mr. James Leslie, Civil Engineer, in his paper on the flow of 
water through pipes, read before the London Institution of 
Civil Engineers, and in part printed for their use, mentions 
several experiments made by him on the rates of delivery of the 
Edinburgh mains. 

In the same pamphlet, Mr. James Simpson, the President of 
the Institution, gives the result of some experiments made by 
himself on the water deliveries of pipe lines of different 
diameters. 

Some of these are presented in Table M, for the purpose of 
comparison. 

In these experiments the deliveries given, generally agree 
very tolerably with the established formulas given in our Table. 

The delivery of the Edinburgh pipe is an exception. 

I am not able to give sufficient reasons why these experi¬ 
ments of Mr. Simpson and others should correspond quite 
nearly with the formulas, from which our experiments differ so 
importantly. 

The good condition of the pipes as respects corrosion, sedi¬ 
ment and collections of air, would probably in a great measure 
explain the difference. 

The pipes experimented on by Mr. Simpson carry the hard 
waters of the London Basin, which do not produce tubercular 
corrosion; they were probably clean pipes of their original 
capacity: the New York pipes carry soft water, and show al¬ 
ready considerable tubercular incrustation. 

The old Crawley pipe of Edinburgh is effected in the same 
way, as are also the Jersey City mains. 

I had hoped to have been able to use the modified formula 


16 


proposed by Mr. Leslie, and found to agree so well with the 
experiments detailed by him, but it does not correspond suffi¬ 
ciently nearly with the results of our experiments on the Croton 
and Jersey City pipes, made under the ordinary every-day con¬ 
ditions of their water deliveries. 

Respectfully submitted, 

JAMES P. KIRKWOOD. 


17 


NOTE 1. 

Conditions of an Experiment made by George S. Greene, Esq., 

Civil Engineer, to ascertain the rate of flow of the water passing 

through the two 36 inch mains situated between the Receiving 

Reservoir of the Croton Works, and what is called the Distribut¬ 
ing Reservoir at Forty-second Street, JVew York City. 

The length of each main is 11,217 feet. 

There are three horizontal curves on each main of 90° each; 
each curve is about 90 feet radius. 

The grade of the avenue on which the pipes are laid undu¬ 
lates considerably, but there exists no abrupt vertical curvature. 

The Receiving Reservoir is divided into two divisions by an 
earthen embankment. 

The southern division was the one used in this experiment, 
and when the Receiving Reservoir is mentioned here it is to be 
understood as the southern division of that Reservoir simply. 

The Distributing Reservoir is also divided into two apart¬ 
ments, but they were used as one in this experiment. 

During this experiment the “ Receiving Reservoir ” was re¬ 
ceiving no water from the Croton Conduit, the sluice gates 
having been all shut down some hours before the commence¬ 
ment, nor from any other source: and no water passed out of 
it except through the two 36 inch mains which are laid in the 
Fifth Avenue; the stop-cocks of the other mains communicating 
with it were shut down. 

All connections with the two 36 inch mains were shut down, 
and the mains themselves were open only for delivery of water 
into the Distributing Reservoir. 

The Distributing Reservoir received no water except from 
these two 36 inch mains. 

From the southern side of this Reservoir, two similar 36 
inch mains were open delivering water into the city. 

These were the only mains open to the passage of water out 
of the Distributing Reservoir. 

The water in this Reservoir rises every night from three to 
five feet, and falls proportionately every day, the consumption 

2 


18 


of water by the city being less during the night than the Res¬ 
ervoir’s receipt of water from above; and more during the 
day. 

The experiment was made on Saturday the 10th of July, be¬ 
tween the hours of 10 A. M. and G P. M. 

During the eight hours above mentioned, the Receiving Res¬ 
ervoir fell 2.16 feet, and delivered into the Distributing Res¬ 
ervoir (=21.204 cubic feet per pipe, per 
second). 1,221,328 cub. ft. 

During the same time the water fell in the 
Distributing Reservoir (which is small com¬ 
pared with the other Reservoir) 3.448 feet. 

The two city pipes on the south side were 
therefore drawing off more from the Forty- 
second Street Reservoir than it was receiving 
by the two pipes delivering into it from the 
upper Reservoir. 

The delivery into the city in excess of the 
amount received here was, by calcula¬ 


tion, . 72,875 “ 

Total delivery from the Distributing Reser¬ 
voir into the city during the eight hours 
aforesaid by the two 36 inch effluent 
pipes.. 1,294,203 “ 


Delivery into the city by one of these pipes 

in the same* time. 647,101.5 “ 


Delivery in twelve hours of the day (6 A. M. 

to 6 P. M.) at same rate. 970,652 “ 

Delivery during the twelve hours of night, 


from 6 P. M. to 6 A . M., taken at one 

fourth of that for the twelve day hours. 242,663 “ 

1,213,315 “ 


Equal to, in New York gallons. 9,479,023 

The second 36 inch effluent main, the same . 9,479,023 
















19 


Besides the two 36 inch mains delivering 
water into the city from the Distributing Res¬ 
ervoir, there are two 30 inch mains which 
deliver into the city directly from the “Re¬ 
ceiving Reservoir.” 

I will suppose these 30 inch mains, (act¬ 
ing under the same head here as the 36 inch 
mains,) to' deliver in such proportion to their 
diameters as the formula prescribes, or as Vd 5 . 

This gives for one 30 inch main a delivery of 6,009,113 
And for the other the same. 6,009,113 

Total estimated consumption of New York 

City per twenty-four hours.30,976,272 galls. 


Equal to 24,781,019 imperial gallons, equal to 3,964,963 
cubic feet. 

The only point in these calculations which is assumed and 
not well ascertained from experiment, is the consumption of 
water during the twelve night hours, viz.: from 6 P. M. to 
6 A. M. 

I have judged this to amount to one quarter of the day con¬ 
sumption. 

But Mr. Greene believes that it amounts to at least one 
third. On account of the inconvenience which the lowering of 
the Reservoir a few feet produces to the consumers in the high 
parts of the city, we refrained from continuing the experiment 
through the whole twenty-four hours. 

The two pipes (36 inch) laid over the Harlem High Bridge, 
when empty of water in October last, were examined inside 
and found to be very considerably encrusted with tubercles. 

These tubercles were generally conical in shape, and varied 
from one quarter to five eighths of an inch in height. 

The pipes experimented on between the two Reservoirs have 
not been examined, that I am aware of, with this view since 
they were laid; but as they have been in use as long as these 
pipes over the High Bridge, and the water passes through them 
at a less velocity, they are probably corroded in the same way. 







20 


NOTE 2. 

Report by C. W. Boynton , Assistant Engineer , of an experiment 

upon the cast iron main leading from the Receiving Reservoir 

to the Distributing Reservoir of the Jersey City Water Wor/cs. 

The object of this experiment was to ascertain the amount of 
water flowing in a given time from one of these Reservoirs to 
the other, and consequently the discharging capacity of the 
connecting main. 

It will be necessary to give a general description of the rela¬ 
tive situations of the Reservoirs and of the pipe line. 

The Receiving Reservoir, situated on the elevated land east 
of the Passaic River, near Belleville, was the basin in which 
the quantity of water passing through the pipe was measured. 

The dimensions of this Reservoir were obtained by a survey 
of its flowage line at an elevation of 157* feet above high water 
in the Passaic River. 

The slopes of the Reservoir are covered with brick laid in 
cement, and their inclination is 1^ to 1. 

Through the kindness of Mr. G. H. Bailey, Chief Engineer of 
the Jersey City Water Works, we have the following informa¬ 
tion in regard to the connecting main. 

The main is enlarged by a mouth piece, at the Receiving Res¬ 
ervoir, to a form very nearly that of the contracted fluid vein, 
so that there is no obstruction to the free discharge of the 
water there. 

The entire length of the main is 29,715 feet, of which all but 
128 feet, where the pipe is turned downwards as an inverted 
syphon beneath the draw at the Hackensack River, is 20 inches 
in diameter; the remainder having a diameter of 24 inches. 


*This is upon the supposition that the 130 feet mark on the guage rod at the 
Pipe Tower of the Distributing Reservoir, the point to which I referred my levels, 
is accurately 130 feet above high water in the Passaic. 



21 


In this main there are the following curves: 

IN THE PORTION OP 20 INCHES DIAMETER. 


Radius of Curve. 

Amount of Deflection. 


Feet. 




3 

90° 



20 

96° 



25 

38° 

30' 


60 

70° 



180 

42° 



200 

79° 



950 

32° 


Unknown ) 
but over ) 

200 

22° 

30' 


IN THE PORTION OF 24 INCHES DIAMETER UNDER THE DRAW 
AT THE HACKENSACK RIVER. 


Radius of Curve. 

Amount of Deflection. 

Feet. 


4.9 

90° 

4.9 

90° 

4.9 

90° 

4.9 

90° 










22 


The Distributing Reservoir is situated upon Bergen Hill, in 
Hudson City. 

The ends of the connecting main in both Reservoirs were 
covered with water, and therefore the difference of level be¬ 
tween the surface of the water in the two Reservoirs at any 
time, gave the head under which the discharge was then taking 
place. 

The difference in elevation of two fixed points, one at each 
Reservoir, was carefully determined by levelling between them, 
and the surface of the water was, at its various elevations, re¬ 
ferred to these points. 

At the Receiving Reservoir, a portion of the well of the gate 
house was separated by a temporary partition from the re¬ 
mainder. 

This partition extended below the water surface sufficiently 
far to prevent the disturbance of the latter, in the separated 
portion, by currents of water entering the main, and still per¬ 
mitted free communication from below with the main part of 
the well, so that the water would maintain the same level inside 
the partition as in the Reservoir itself. 

Within the part of the well thus separated the elevation of 
the water surface was determined, during the experiment, by 
means of a float and attached guage staff. 

The height of the water surface was also noted outside of 
the gate house by measurement with a levelling rod, (when 
darkness did not prevent,) and the records were found to agree 
very nearly with the first measurement. 

The mean of both observations was the one used in arriving 
at the result. 

At the Distributing Reservoir observations were taken from 
the guage rod on the pipe tower. 


23 


The following are the recorded observations at the two 
Reservoirs: 


At the Receiving Reservoir. 

At the Distributing Reservoir. 

Time of Observation. 

Elevation 
of Water 
Surface. 

Time of Observation. 

Elevation 
of Water 
Surface. 

Sept. 25th, 1858. 

Feet. 

Sept. 25th, 1858. 

Feet. 

6h 33±m, A.M. 

155.029 

6h 00m, A.M. 

124.5 

*7h 16m, “ 

154.989 



nih 33|m, “ 

154.669 



12h 16m, P.M. 

154.482 

12h 00m, M. 

124.48 

5h 16m, “ 

153.992 

6h 00m, P.M. 

124.48 

9h 16m, “ 

153.614 

Sept. 26th. 


Sept. 26th. 


6h 00m, A.M. 

124.54 

12h 16m, P.M. 

152.166 

12h 00m, M. 

124.56 

6h 16m, “ 

151.604 

6h 00m, P.M. 

124.604 

Sept. 27 th. 


Sept. 27th. 


7h 29m, A.M. 

150.356 

6h 00in, A.M. 

124.71 


The annexed Table I gives a statement of the information 
obtained by the experiment. 

Column (1) contains the recorded elevations of the water 
surface at the Receiving Reservoir. 

Column (2) is obtained by calculation from the dimensions 
of the Reservoir. 

Column (3) gives the difference between the elevations in 
column (1). 


* These observations, taken so near the time of the preceding and following 
ones, are not used in calculating the result. 

















24 


Column (4) contains the quantities discharged from the Res¬ 
ervoir, as calculated from columns (2) and (3). 

Column (5) gives the difference in the recorded times of ob¬ 
servation. 

Columns (6), (7) and (8) need no explanation. 

Column (9) is obtained by subtracting from the elevation of 
the water surface in the Receiving Reservoir, the elevation of 
the surface of the water in the Distributing Reservoir at the 
same time, as deduced from the observations made at the latter, 
which, it will be seen, were not simultaneous with those at the 
Receiving Reservoir. 

Column (10) is obtained from column (9) by the formula 


h= 


VH,+ VH. j* +A 


Where H,=tlie head at the commencement of the discharge. 

H 2 = “ “ end of the discharge, 

h =mean head under which the discharge occurs, 
and A =the distance of the centre of gravity of the water 
prismoid above the middle point of its altitude. 

Some discrepancies will be observed in the results of the 
Table; these were doubtless caused by small errors in the deter¬ 
mination of the elevations of the water surface. Such could 
hardly be avoided without more accurate means of measurement 
than were at onr disposal. 


It remains to compare our results with those obtained from 
the various formulas in ordinary use for determining the dis¬ 
charge of water through pipes. 

The following have been considered the most reliable. 

As expressed by their authors, the units employed are various, 
but for convenience in comparison and calculation, I have re¬ 
duced all to their equivalent expressions in English feet.* 

(Jl.) Hawkesley’s. v=4S.0125^-ii_- ] 

See Civil Eng. and Architect's Journal, Vol. XVIII., p. 99, line 28. 


* In these reductions I have taken 

The French metre=3.28089 English feet. 
“ Prussian Foot= 1.02972 “ 








Tabular Comparison of the New York and Jersey City Experiments. 


K. 


EXPERIMENTS: 

Where, and by whom, made. 

J Diameter of the 


Mean Heads 
under which the 
discharge occurred. 

VALUES OF THE VELOCITY, IN FEET PER SECOND. 

Pipe, in feet. 

Length of Pipe, 
in feet. 

As deduced from 
the discharge. 

By Hawkesley’s 
formula. 

w 

By Blackwell’s 
formula. 

(B.) 

By Prony’s 
formula (1). 

( c■) 

By Prony’s 
formula (2). 
(D.) 

By Eytelwein’s 
formula. 

(E.) 

By D’Aubuisson’s 
formula (1). 

m 

By D’Aubuisson’s 
formula (2). 
(G.) 

By Weisbach’s 
formula. 

(H.) 

On the 20 inch Main between the Reservoirs 

. 1.6667 

29,715 

30.262 

1.4924 

1.97399 

1.97624 

1.9206 

1.91068 

1.97063 

1.927302 

1.92923 

2.03255 

of the Jersey City Water Works. 

\ 1.6667 

29,715 

29.758 

1.51337 

1.9575 

1.9597 

1.9039 

1.89338 

1.95416 

1.9105 

1.9123 

2.01294 

By O. H. Bailey and C. W. Boynton. 

J 1.6667 

29,715 

29.817 

1.44893 

1.94293 

1.94514 

1.8891 

1.87838 

1.93963 

1.8957 

1.8976 

1.99688 

128 feet of this Main is 24 inches diameter. 

1.6667 

29,715 

28.365 

1.45795 

1.91112 

1.9133 

1.8570 

1.8453 

1.90789 

1.8632 

1.8650 

1.95938 

Allowance is made in the calculation for this 

/ 1.6667 

29,715 

27.302 

1.39107 

1.8750 

1.877115 

1.8204 

1.8077 

1.87180 

1.8263 

1.8282 

1.91797 

enlargement, and the curves in the pipe. 1 

1.6667 

29,715 

26.325 

1.381155 

1.84115 

1.84323 

1.7861 

1.7726 

1.83801 ' 

1.7918 

1.7936 

1.87943 

Jersey City Water Works. Mean result. 

1 

1.6667 

29,715 

28.1285 

1.43795 

1.90031 

1.9053 

1.8489 

1.837 

1.8999 

1.855 

1.857 

1.9502 

































































































25 


(B.) Blackwell’s. v=47.913 I— 

V L 

This formula takes into account the curves of the pipe. 

See Hughes on Water Works. Formula (33 ),p. 336. 

(C.) Prony’s (1). v=^(2354.9375^ +0.00665)-0.0816. 

See Prongs Recherches Physico—Mathimatiques sur la thiorie des Eaust 
Courantes, § 184. 

(D.) Prony’s (2). v=^(2494.69^+0.02375)-0.15412. 

See Prony’s Recherches Physico—Mathimatiques sur la thiorie des Eaux 
Courantes , § 210. 

( E .) Eytelwein’s. v=47.8731 /_ — _ 

V L+54d 

See Memoires de I’Academie des Sciences de Berlin, 1814 et 1815, p. 165. 

(F.) D’Aubuisson’s (1). 

v _ / h 0.00003767485r 1* 

v 0.0004X75685.+ [0.015536] + 0.000417568^+ [0.015536] 

0.00003767485j- 
0.000417568^+[0.015536] 

See D’Aubuisson’s Hydraulics , (Bennett’s translation,) p. 206, top. 


(G.) D’Aubuisson’s (2). v= i y(2394.82^+0.00814)-0.090224 


See Neville’s Hyd. Formula (109j, p. 118. Simplification of [i* 7 ], by omit¬ 
ting the constant [0.015536], and reducing. 


( H .) Weisbach’s. 

h—0.015538v® =0.015538—*— ^ 0.01439+ °°^_ — j 

See Julius Weisbach’s lngenieur und Maschinen Mechanik. Vol. /., p. 748. 


In all the above 

v=Velocity, in feet per second. 
h=the Head, in feet. 
d=Diameter of pipe, in feet. 
L=Length of pipe, in feet. 















26 


None of these formulas except Blackwell’s [B], which takes 
into account the curves, make any allowance for changes of 
direction or capacity of the pipe. 

In the Jersey City main there are no abrupt bends, and for 
the determination of the loss of head by the curves, I have em¬ 
ployed the formula of Julius Weisbach. 

h -=lfo X (o.m+1.847(^)-g 

See Weisbach's Ingcnieitr und Maschinen Mechanik. Vol. /., p. 770. 

When h c =Head lost by the resistance of the curves, in feet. 

$=the deflection of the pipe from its right line di¬ 
rection, in degrees. 

r=the radius of the interior of the pipe, in feet. 

R= the radius of curvature of the axis of the pipe, in 
feet. 

v=the Telocity of the water passing through the 
pipe, in feet per second. 

g=32.18=acceleration due to gravity. 

By means of this formula the values of the total loss of head 
from curves in the pipe has been calculated for as great a range 
of velocities as will result in the use of the formulas above em¬ 
ployed for their calculation. 

These are inserted in the following Table. 


Table 2. 


Y alues of the T elocity. 

1.7 

1.8 

1.9 

2.0 

2.1 

Total loss of head from 
resistance of curves. 

0.0218 

0.0244 

0.0272 

0.0302 

0.0333 


The enlargement of the pipe in passing the draw at the 
Hackensack River, and its subsequent contraction, are made by 
means of reducers, five feet long, and therefore the change in 
velocity is so gradual that we may consider the loss of head 
from this cause inappreciable. 












27 


We have* however, a gain of head, equal to the difference 
between the head lost by the friction of the water in passing 
through 128 feet of 20 inch, and the same length of 24 inch 
pipe. 

This difference I have calculated, by Weisbach’s formula [H], 
for various velocities of the water in the 20 inch pipe, and the 
values thereof are appended in the following Table. 


Table 3. 


Velocity of the water 
in the 20 inch pipe. . 

v= 1.7 

v=1.8 

v=1.9 

v=2.0 

v=2.1 

Gain of head of 128 ft. 
of 24 inch pipe over 
the same length of 
20 inch pipe. 

0.0532 

0.0589 

0.0648 

0.0710 

0.0774 


Since the loss of head by the influence of the curves, and its 
gain by the enlargement of the main, depend for their value 
upon the velocity of the water in the pipe, it is necessary in 
employing any of the above formulas for finding the velocity, to 
first calculate the latter approximately, by the formula which 
we intend using, neglecting in this calculation the influence 
upon the head of the curves and enlargements. 

The velocity being in this manner determined, Tables (2) 
and (3) give the correction to be applied to the head; that ob¬ 
tained from (2) being a subtractive, and that from (3) an addi¬ 
tive correction. 

From this corrected head a closer approximation to the 
velocity is obtained by the formula. 

The value of the velocity thus resulting, gives us more nearly 
the value of the resistances of curves and enlargements, and 
thus a still more accurate value of the corrected head, from 
which, by again applying the formula, a value of the velocity is 















28 


obtained sufficiently accurate for comparison with the results of 
the experiment. 

These values of the velocity have been calculated by all the 
formulas above given, and the results, together with those de¬ 
rived by actual experiment, are inserted in the accompanying 
tabular statement marked K. 


[A.) Hawkeslev’s. v=48.0125 /— 

Vi, 


hd 


(+54d 

See Civil Eng. and Architects' Journal , Vol. XVIII., p. 09. line 2 


(B.) Blackwell’s. v=47.913 /— This formula takes inti 

V L 

See Hughes on Water Works. Formula (33). p. 336. 


(C.) Prony’s (1). v= /(2354.9375^+0.00665)-0.0816. 

V v L 

»S*r Prony's Recherches Physico—Mathematiques sur la theorie d 


(D.) Prony’s (2). v= /(2494.69—+ 0.02375)-0.15412. 

V L 

See Prony's Recherches Physico—Mathematiques sur la theorie d< 


(E.) Eytelwein’s. v=47.8731 I— 

V L4-1 


-4-54(1 

-SVe Memo ires de VAcademie des Sciences de Berlin, 1814 et 1815, 


(F.) D’AulmissoiTs (1). v= A /--—- 

v 0.000417568k 


[0.015536] 1 

See D'Aubuisson's Hydraulics , (Bennett's translation.) p. 20(1, top 


( G .) D’Aulmisson’s (2). v= /(2394.82^+0.00814)-0.09 

See Neville's Hyd. Formula (l()9),p. 118. Simplification of [F] 


.o r v 

(II.) Weisbach’s. h-0.015538v* =0.01553844 0.01431 

See Julius Weisbach's Ingenieur and Maschinen Mechanik. Vol 
























29 


NOTE 3. 

Extract from Proceedings of Institution of Civil Engineers , Lon- 1 
don , February , 1855. 

“ Mr. Murray had prepared the following table, showing the 
delivery of water, by pipes of small and of large dimensions, 
through moderate and more extended lengths and under vari¬ 
ous pressures, and he contended, that far from throwing dis¬ 
credit upon the researches of the experimenters, whose works 
he had mentioned, the accuracy of the formulas had been satis¬ 
factorily confirmed by practice. 


DISCHARGE THROUGH PIPES, CALCULATED BY SEVERAL FORMULAE. 


Diameter 

of 

Pipe. 

Length. 

Head 

or 

Pressure. ! 

Discharge 

per 

Minute. 

Calculated 
Discharge 
per Minute. 


INCHES. 

2 

FEET. 

3,300 

FEET. 

12.75 

CUB. FEET. 

1.617 

CUB. FEET. 

1.507 

Du Buat. 


• • • • 



1.609 

Prony. 

•. • • 




1.509 

Eytelwein. 





1.59 

Poncelet. 

4 1 

% 

1*4,930 

51.00 

ii.*3*33 

11.252 

Du Buat. 



11.491 

Prony. 


.... 



10.784 

Eytelwein. 


.... 


_ 

11.281 

Poncelet. 

12.789 

3,837 

1*2*90 

j 155 

158 

Du Buat. 


• • • • 



155 

Prony. 

.... 

• • • • 

• • • • 

.... 

145 

Eytelwein. 





141 

Poncelet. 

12.789 

1*4,963 

21.582 

lii 

99 

Du Buat. 


.... 



102 

Prony. 

.... 


• • • • 


99 

Eytelwein. 





98 

Poncelet. 

19. i 84 

5,052 

4.929 

217 

223 

Du Buat. 


.... 



230 

Prony. 


.... 

.... 


215 

Eytelwein. 





226 

Poncelet. 

30 

*5*280 

*9.00 

880*’ 

926 

Du Buat. 


.... 



932 

Prony. 


• • • • 

.... 

| 

865 . 

Eytelwein. 


.... 

.... 

l .... 

910 

Poncelet. 


















30 


In explanation of the Table it was stated, on the authority 
of Dr. Robinson, (vide Robinson’s ‘ Mechanical Philosophy,’ 
vol. ii, p. 441) that water was brought into the town of Dun¬ 
bar, in East Lothian, from a spring, through pipes, the first 
length of which was 1,100 yards, of 2 inches diameter, with a 
declivity of 12 feet 9 inches. 

The actual quantity discharged was 1.017 cubic foot per 
minute. The mean calculated quantity was 1.5539 cubic foot 
per minute. 

Again it was shown by Mr. Jardine, (vide Brewster’s Ency¬ 
clopaedia; Art. ‘ Hydrodynamics,^ p. 526) that the main pipe 
of the Edinburgh Water Works, extending from the fountain 
head, at Comiston, to the reservoir at the Castle Hill, Edin¬ 
burgh, was of lead throughout, 14,950 feet in length, 4^ inches 
in diameter, and the head was 51 feet above the point of deliv¬ 
ery. The maximum discharge during five consecutive years, 
was 11.333 cubic feet per minute. 

The mean calculated quantity was 11.202 cubic feet per 
minute. 

The next three results were taken from Bossut’s ‘ Treatise on 
Hydrodynamics ’ brought into English measures, and they were 
stated to be his own experiments, combined with those of 
Couplet. The pipes were of iron with several horizontal and 
vertical bends, which were taken into account in the lengths 
mentioned:— 

Cubic Feet Mean calcu- 
per Minute, lated quantity. 


The first yielded.155 150 cub. ft. per min. 

The second “ .Ill 99.5 “ “ 

The third “ .217 223.5 “ 


The last statement of the table was obtained from the late 
Mr. Chapman, C. E., of Newcastle; but whether it was de¬ 
rived from actual measurement, or was simply the result of his 
experience, was uncertain. From a pipe of 30 inches diameter, 
with a fall of 9 feet per mile, the actual quantity discharged 
was 880 cubic feet per minute. 

The mean calculated quantity was 908 cubic feet, per minute. 

The following were the formulae employed in the calculations 
of the table:— 







31 


Du Buat’s Formula reduced to English Measure 

—0.8( VR—0.1) 


y _307(VR-0.1) 


VS-L( VS+1.0) 

V = velocity in inches per second. 

R=hydraulic mean depth=J diameter. 

*S=slope or difference of level. 

L=hyperbolic logarithm, and found by multiplying the com¬ 
mon logarithm by 2.3026. 


In the following formula} English feet were employed :— 
V being the velocity per second. 

D “ diameter ) 

H “ head of pressure, > of the pipe. 

L “ . the length ) 

Prony’s simple Formula. 

V=48.449 


Eytelwein’s Formula, as given by Tredgold (vide Tredgold’s 
‘Tracts on Hydraulics/ p. 215.) 

V=45.5 OH 
V L+47D 

Poncelet’s formula. 


V = 47.95 /_ 
VL 


DH 


VL+54D 


* The explanation of the value of S here given, is, as will be evident by an ex¬ 
amination of the formula, erroneous. 

e Length of the pipe. 

Really 

Head of pressure. 










32 


NOTE 4. 


The following (furnished me by J. C. Brevoort, Esq.) is the 
formula proposed by M. Mary, of the French Academy of 
Sciences, for determining the flow of water in pipes: 



Where v = Velocity, in feet per second, 
h = the Head, in feet, 
d = Diameter of the pipe, in feet. 

L = Length of the pipe, in feet. 

C = a Constant which varies with the velocity, and 
the values of which are obtained from the fol¬ 
lowing Table. 


Values of 

V. 

0.164 

0.328 

0.656 

0.984 

1.312 

1.640 

3.281 

6.562 

Infinity. 

Values of 
C. 

34.723 

39.722 

43.417 

44.975 

45.753 

46.297 

47.420 

47.945 

48.470 


In the use of this formula, the value of v is obtained by ap¬ 
proximation. A mean value of C being first assumed, the value 
of v is approximately calculated, which gives us more accurately 
the value of C; thence results a value of v more nearly correct 
than the preceding. 

By two or three applications of the formula, in this manner, 
the value of v is deduced with sufficient accuracy. 
















Ft F T H AVENUE: 



shewing theposition of 

CERTAIN WATER PIPE MAINS 

in the City of 
5E\Y YORK 

October 1858 . 

Scale of Feet 





Reference 

Thirty sue inch Pi/it ■ shewn thus 

Thirty „ . , • 

Twenty , , - » 

Tire/x-e , , . » 

Six- , 

Connections 


+ 





























































The sur/erce water ttfthis Ttcseriwir, 
w/teti/JuU,iir /57fift afipre Aiyh water 
in, the, fiasscue //ever. ' 


> ^ 


’limping; laimne 


0=0fc 





irrch /'t/ip eene/er /hr d/vrer a/ /hr J/arhr// .rar/r Itiver 
State tii 


JLechtcerJmm 2Vtr 20 " 




DIAGRAM 

shewing the/ r&latwe /wsitwns 

of the 

RESERVOIRS and CONNECTING MAIN 

JERSEY CUTWATER WORKS. 

October 1858. 







TjverUtj inch Pifu , shewn, - 

Twenty four in. do. " ” ___ 


SCALE or FEET 

1 _tl 


'% s 



/ 






0 Sarin 












































> 

LIBRARY OF CONGRESS i 




















































































































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